Abstract
Using the notion of the Łukasiewicz fuzzy set, we study the filter theory of Sheffer stroke Hilbert algebras. Here’s what we’re trying to do. 1. We first introduce the Łukasiewicz fuzzy filter of Sheffer stroke Hilbert algebras. 2. We provide an example to illustrates the Łukasiewicz fuzzy filter. 3. We examine the various properties of the Łukasiewicz fuzzy filter. 4. We discuss characterizations of the Łukasiewicz fuzzy filter. 5. We explore the conditions under which Łukasiewicz fuzzy set can be Łukasiewicz fuzzy filter. 6. We discuss the relationship between fuzzy filter and Łukasiewicz fuzzy filter. 7. We use the given filter to creates a Łukasiewicz fuzzy filter. 8. We present conditions for the three subsets, called ∈-set, q-set and O-set, to be filters.
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